All Questions

I'm trying to understand how bad things could possibly get without Cauchy completeness as a criterion for Hilbert spaces in quantum mechanics. Obviously, doing calculus on a pre-Hilbert space would be ...

According to the papers The absolutely continuous spectrum of Jacobi matrices and these lecture notes: periodicity ~ potential well or lattice (order) lack of absolutely continued spectrum ~ Anderson ...

In infinite spectral theory, we have the discrete and continuous spectrum, which are called "bound" and "scatter states" in physics. My understanding is, if $O \in B(H)$ is a self-...